We present here the results of a series of molecular dynamics (MD) simulations of systems of soft repulsive tapered particles. Essentially, the objective of the project was to investigate the effect that changing the degree of taper of these particles has on the collective behaviour of the system. The particle shapes were modelled using the parameterised Gaussian overlap (PHGO) contact function, which had previously been used in Monte Carlo (MC) studies of systems of hard particles with the same range of shapes [Phys. Rev. E 68,021708 (2003)]. The work carried out falls into three main categories. Firstly we calculated the splay and bend reduced flexoelectric coefficients, e11 and e33, for a number of systems in the nematic phase. This was done using the linear response approach developed by Nemtsov and Osipov [Kristallografiya 31 2,213-218 (1986)]. The values of e11 measured for the tapered systems studied were all positive and of the order of +0.1, whilst the e33 values were of a similar magnitude but negative in all cases. These numbers correspond to values of the order of pCm-1, which is consistent with typical values measured experimentally for the flexoelectric coefficients. The reduced coefficients for systems of uniaxial particles were also calculated and found to be approximately zero, as they should be for particles with this type of symmetry. The second major theme in the project was the mapping out of the shape-density phase diagram, through both compression and decompression sequences, for tapered particles having a constant length to breadth ratio of 3 but different degrees of tapering, ranging from an extreme tear-drop shape to the uniaxial Gaussian ellipsoid. The results of our MD simulations broadly agreed with those obtained by the MC route [Phys. Rev. E 68,021708 (2003)]. Isotropic, nematic, smectic and ordered solid phases were clearly identified. In addition a so-called `curvy-bilayer' (CB) phase was observed, which locally possessed similar order to the smectics but did not exhibit any clear long range order. The structure of the CB phase was investigated further and found to be a type of bicontinuous cubic phase, specifically the Ia3d or gyroid (G) as it is also known -a phase never before obtained from this type of simulation. Characterisation of the I-G transition was undertaken, which indicated that the gyroid freely selfassembled from precursors present in the isotropic fluid. The Sm-G transition was also characterised and found to take place via the formation, firstly of stalks joining two adjacent smectic bilayers and then subsequently pores which bisect these bilayers and initiate the emergence of the gyroid morphology.